It is my experience that not all Platinum members are treated equally. A colleague of mine who doesn't stay all too often at Starwood just manage to make Platinum last year and was given a personal concierge yet I was never given that option although I have triple the nights he has. The same is true of another friend of mine.
I have inquired with Starwood regarding this over 5 weeks ago and have yet to hear from them.
Some of the concierges are extremely talented and a personal concierge can be very helpful in many ways but alas I could only tell you second hand from my colleague and friend.
My advice is to use your personal concierge since you have one and I don't think they will consider it a bother when you do call.